Testing for new is better than used in expectation

Abstract

A class of tests which are usually believed to be the tests of exponentiality vs. increasing failure rate (IFR) alternatives are shown to be consistent against a class of NBUE alternatives - a much larger class than IFR. Moreover a comparison is made of the Bahadur efficiency of the total time on test statistic W with the Kolmogorov-Smirnov statistic D. It is found that the D-test has larger exact slope at least favorable IFR distributions which are close to the exponential and also at pure NBUE distributions close to the exponential than does the W-test statistic, whereas the reverse is the case at Weibull (8), 6 > 1.